I ask my students to show their work; it is primarily so that I know they didn’t cheat, but secondarily so that I know they didn’t just guess. At my level I don’t really care which method they use to get their answers, but in K-12 “math” is mainly a suite of algorithms, and it is reasonable for students to be able to show they have mastered the algorithms. While there are big differences between curricula from one school to another (or one decade to another), the algorithms don’t change all that much.
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